Question

If ∫df(x,y)da=7, where d is the triangular region with vertices (0,0),(2,0), and (2,2), find the average value of f(x, y) on d. give your answer correct to 2 decimal places.

Answer 1

To find the average value of f(x, y) on the triangular region d, divide the integral of f(x, y) over d by the area of d.

Step-by-step explanation:

To find the average value of f(x, y) on the triangular region d, we need to find the total value of the function integrated over the region and divide it by the area of the region. We are given that ∫df(x,y)da = 7 for the region d. The formula for average value is Avg = (1/Area) * ∫f(x,y)da. Therefore, we need to find the area of the triangular region d and divide 7 by that area to get the average value.